For the Planck function I„(T) (see equation 5.86), what is the most probable frequency Vp at a given temperature T? For the Planck function expressed as a function of wavelength, I,(T) (see equation 5.90), what is the most probable wavelength p at a given temperature T? For what range of temperatures does , fall in the visible range of the electromagnetic spectrum?
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- What is the energy density U/V of a photon gas at (a) room temperature (T = 295 K), and (b) at a temperature 50 times larger? (a) The energy density U/V of a photon gas at room temperature (T = 295 K) is _____ Jm3 (b) The energy density U/V of a photon gas at a temperature 50 times larger than the room temperature is ________Jm3A cavity radiator has its maximum spectral radiance at a wavelength of 2,5×10-7 m. If the body is heated so that T/T0 = 5,5, what will be the ratio of radiant powers W/W0? Wien's constant b = 2.897 ×10-3 m·K.Outline the steps leading to the formula for the number of photons with angular fre- quencies between w and w + dw in blackbody radiation at a temperature T: w? dw V n(w)dw = 2 x 272c3 ehw/kBT Show that n(w) has a peak at a frequency given by w = 1.59kgT/h. Show further that the spectral energy densities ux and uw peak at Amax = hc/(4.97KBT) and wmax = 2.82KBT/ħ, respectively.
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